WO2022225543A1

WO2022225543A1 - Electrode design for lumped opto-electric modulator

Info

Publication number: WO2022225543A1
Application number: PCT/US2021/044176
Authority: WO
Inventors: Hongbing Lei; Xiao Shen; Karthikeyan Krishnamurthy; Chunlei LIAO
Original assignee: Futurewei Technologies, Inc.
Priority date: 2021-04-22
Filing date: 2021-08-02
Publication date: 2022-10-27

Abstract

A method of designing a lumped optical modulator is disclosed. A candidate electrode length is selected for an electrode in the lumped optical modulator. A driving position is determined between a proximate end of the electrode and a midpoint of the electrode. The driving position is determined to result in a maximum electro-optical bandwidth for the candidate electrode length. The candidate electrode length is adjusted when a desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length. The candidate electrode length and the driving position are selected when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

Description

Electrode Design For Lumped Opto-Electric Modulator

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This patent application claims the benefit of U.S. Provisional Patent Application No. 63/178,336, filed April 22, 2021 by Hongbing Lei, et al., and titled “Radio Frequency (RF) Electrode Design For Single/Multi-Segmented Lumped Modulator To Enhance Opto-Electric (OE) Bandwidth,” which is hereby incorporated by reference.

TECHNICAL FIELD

[0002] The present disclosure is generally related to Silicon (Si) based optical network communications, and more particularly, to a mechanism for selecting a driving position of an electrode in a lumped optical modulator to enhance opto-electric (OE) bandwidth.

BACKGROUND

[0003] Silicon (Si) based photonics uses silicon as an optical medium. The silicon may be patterned into microphotonic components with sub-micrometer precision. These components may operate in the infrared spectrum, for example at the wavelengths used by many fiber optic telecommunication systems. The silicon typically lies on top of a layer of silica known as silicon on insulator (SOI). Silicon photonic devices can be made using semiconductor fabrication techniques. Because silicon is already used as the substrate for most integrated circuits, hybrid devices may be created to integrate the optical and electronic components onto a single microchip. Silicon photonics are generally used in coherent fiber communications and/or short- reach application up to 64 Giga-baud (Gbaud) frequencies. However, silicon photonic devices may suffer from certain bandwidth limitations.

SUMMARY

[0004] In an embodiment, the disclosure includes a method of designing a lumped optical modulator, the method comprising: selecting, by a processor, a candidate electrode length for an electrode in the lumped optical modulator; determining, by the processor, a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro-optical bandwidth for the candidate electrode length; adjusting, by the processor, the candidate electrode length when a desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and selecting, by the processor, the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

[0005] Lumped optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of an optical waveguide. In most lumped optical modulators, a driver amplifier is connected to the electrode at a midpoint. An electrical signal from the driver amplifiers is applied to the electrodes. This changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. The maximum signal frequency that can be supported by a lumped optical modulator is a function of input power, modulator length, electrode length, and driver amplifier impedance. One approach to increase the maximum signal frequency is to split each electrode into multiple discontinuous segments and increase the number of driver amplifiers attached to the electrodes. Accordingly, many parameters of a lumped optical modulator can be adjusted to tune the modulator to a desired set of frequencies. Regardless of the parameter configuration, lumped optical modulators perform poorly at higher frequencies (e.g., greater than 60 gigahertz (GHz)). [0006] The present embodiment includes a method for adjusting an additional parameter to tune a lumped optical modulator to operate at higher frequencies. As noted above, lumped optical modulators include driver amplifiers that are connected to the electrodes at a midpoint. This creates a pair of equal sized radio frequency (RF) cavities in the electrode on either side of the midpoint that resonate at higher frequencies. The disclosed mechanism adjusts the position of the driving connection. This alters the size of the RF cavities, and hence adjusts the resonance frequencies that can be achieved. In order to support phase matching between the electrical signal and the optical carrier wave, the driving position is located between the proximate end of the electrode (nearest the optical carrier wave input) and the midpoint of the electrode. The mechanism selects a candidate electrode length and iteratively tests various driving positions between the proximate end of the electrode and the midpoint. When the desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth achieved by such testing, candidate electrode length can be increased for further testing. When the desired electro- optical bandwidth is within a range of the maximum electro-optical bandwidth, the electrode length and driving position are known. A number of segments can then be determined based on the electrode length and the modulator length. Accordingly, the present disclosure includes an adjustable parameter and a mechanism for adjusting such a parameter to tune an optical modulator for operation at a specified set of higher frequencies without an associated increase in power. Hence, the disclosed mechanisms support an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed mechanisms can be used to create additional functionality, reduce resource usage, and/or solve problems that are specific to optical signal generation and associated component design.

[0007] Optionally, in any of the preceding aspects, another implementation of the aspect provides, further comprising determining, by the processor, a number of electrode segments for the selected candidate electrode length resulting in a segmented electrode of a total length of the lumped optical modulator.

[0008] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the lumped optical modulator comprising an optical input for receiving an optical carrier wave for modulation and an optical output for outputting an optical signal, the proximate end of the electrode positioned toward the optical input and away from the optical output.

[0009] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the determining the driving position comprising: iteratively testing a resulting electro- optical bandwidth for each candidate driving position between the proximate end of the electrode and the midpoint of the electrode; and determining the candidate driving position with a largest resulting electro-optical bandwidth as the driving position resulting in the maximum electro- optical bandwidth for the candidate electrode length.

[0010] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the driving position creating radio frequency (RF) cavities in the electrode that resonate at corresponding frequencies, the iteratively testing comprising determining the resulting electro- optical bandwidth corresponding to resonance of the RF cavities based on RF cavity length. [0011] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the lumped optical modulator not comprising a terminal resistor connected to the electrode.

[0012] Optionally, in any of the preceding aspects, another implementation of the aspect provides, further comprising connecting the electrode to a driving amplifier by a copper pillar, solder ball, or flipchip bonding at the driving position.

[0013] In an embodiment, the disclosure includes a lumped optical modulator designed by a process of: selecting, by a processor, a candidate electrode length for an electrode in the lumped optical modulator; determining, by the processor, a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro- optical bandwidth for the candidate electrode length; adjusting, by the processor, the candidate electrode length when a desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and selecting, by the processor, the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length. [0014] Lumped optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of an optical waveguide. In most lumped optical modulators, a driver amplifier is connected to the electrode at a midpoint. An electrical signal from the driver amplifiers is applied to the electrodes. This changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. The maximum signal frequency that can be supported by a lumped optical modulator is a function of input power, modulator length, electrode length, and driver amplifier impedance. One approach to increase the maximum signal frequency is to split each electrode into multiple discontinuous segments and increase the number of driver amplifiers attached to the electrodes. Accordingly, many parameters of a lumped optical modulator can be adjusted to tune the modulator to a desired set of frequencies. Regardless of the parameter configuration, lumped optical modulators perform poorly at higher frequencies (e.g., greater than 60 gigahertz (GHz)). [0015] The present embodiment includes a mechanism for adjusting an additional parameter to tune a lumped optical modulator to operate at higher frequencies. As noted above, lumped optical modulators include driver amplifiers that are connected to the electrodes at a midpoint. This creates a pair of equal sized radio frequency (RF) cavities in the electrode on either side of the midpoint that resonate at higher frequencies. The disclosed mechanism adjusts the position of the driving connection. This alters the size of the RF cavities, and hence adjusts the resonance frequencies that can be achieved. In order to support phase matching between the electrical signal and the optical carrier wave, the driving position is located between the proximate end of the electrode (nearest the optical carrier wave input) and the midpoint of the electrode. The mechanism selects a candidate electrode length and iteratively tests various driving positions between the proximate end of the electrode and the midpoint. When the desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth achieved by such testing, candidate electrode length can be increased for further testing. When the desired electro- optical bandwidth is within a range of the maximum electro-optical bandwidth, the electrode length and driving position are known. A number of segments can then be determined based on the electrode length and the modulator length. Accordingly, the present disclosure includes an adjustable parameter and a mechanism for adjusting such a parameter to tune an optical modulator for operation at a specified set of higher frequencies without an associated increase in power. Hence, the disclosed mechanisms support an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed mechanisms can be used to create additional functionality, reduce resource usage, and/or solve problems that are specific to optical signal generation and associated component design.

[0016] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the process further comprising determining, by the processor, a number of electrode segments for the selected candidate electrode length resulting in a segmented electrode of a total length of the lumped optical modulator.

[0017] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the lumped optical modulator comprising an optical input for receiving an optical carrier wave for modulation and an optical output for outputting an optical signal, the proximate end of the electrode positioned toward the optical input and away from the optical output.

[0018] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the determining the driving position comprising: iteratively testing a resulting electro- optical bandwidth for each candidate driving position between the proximate end of the electrode and the midpoint of the electrode; and determining the candidate driving position with a largest resulting electro-optical bandwidth as the driving position resulting in the maximum electro- optical bandwidth for the candidate electrode length.

[0019] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the driving position creating radio frequency (RF) cavities in the electrode that resonate at corresponding frequencies, the iteratively testing comprising determining the resulting electro- optical bandwidth corresponding to resonance of the RF cavities based on RF cavity length. [0020] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the lumped optical modulator not comprising a terminal resistor connected to the electrode.

[0021] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the process further comprising connecting the electrode to a driving amplifier by a copper pillar, solder ball, or flipchip bonding at the driving position.

[0022] In an embodiment, the disclosure includes a lumped optical modulator comprising: an optical waveguide comprising a first arm with an optical input and an optical output; and a first electrode positioned adjacent to the first arm, the first electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a first driving connection connected to the first electrode between the proximate end and the midpoint.

[0023] Lumped optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of an optical waveguide. In most lumped optical modulators, a driver amplifier is connected to the electrode at a midpoint. An electrical signal from the driver amplifiers is applied to the electrodes. This changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. The maximum signal frequency that can be supported by a lumped optical modulator is a function of input power, modulator length, electrode length, and driver amplifier impedance. One approach to increase the maximum signal frequency is to split each electrode into multiple discontinuous segments and increase the number of driver amplifiers attached to the electrodes. Accordingly, many parameters of a lumped optical modulator can be adjusted to tune the modulator to a desired set of frequencies. Regardless of the parameter configuration, lumped optical modulators perform poorly at higher frequencies (e.g., greater than 60 gigahertz (GHz)). [0024] The present embodiment includes a mechanism for adjusting an additional parameter to tune a lumped optical modulator to operate at higher frequencies. As noted above, lumped optical modulators include driver amplifiers that are connected to the electrodes at a midpoint. This creates a pair of equal sized radio frequency (RF) cavities in the electrode on either side of the midpoint that resonate at higher frequencies. The disclosed mechanism adjusts the position of the driving connection. This alters the size of the RF cavities, and hence adjusts the resonance frequencies that can be achieved. In order to support phase matching between the electrical signal and the optical carrier wave, the driving position is located between the proximate end of the electrode (nearest the optical carrier wave input) and the midpoint of the electrode. The mechanism selects a candidate electrode length and iteratively tests various driving positions between the proximate end of the electrode and the midpoint. When the desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth achieved by such testing, candidate electrode length can be increased for further testing. When the desired electro- optical bandwidth is within a range of the maximum electro-optical bandwidth, the electrode length and driving position are known. A number of segments can then be determined based on the electrode length and the modulator length. Accordingly, the present disclosure includes an adjustable parameter and a mechanism for adjusting such a parameter to tune an optical modulator for operation at a specified set of higher frequencies without an associated increase in power. Hence, the disclosed mechanisms support an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed mechanisms can be used to create additional functionality, reduce resource usage, and/or solve problems that are specific to optical signal generation and associated component design.

[0025] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the optical waveguide further comprising a second arm with an optical input and an optical output, and the lumped optical modulator further comprising: a second electrode positioned between the first arm and the second arm, the second electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a second driving connection connected to the second electrode between the proximate end and the midpoint.

[0026] Optionally, in any of the preceding aspects, another implementation of the aspect provides, further comprising: a third electrode positioned between the first arm and the second arm, the third electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a third driving connection connected to the third electrode between the proximate end and the midpoint.

[0027] Optionally, in any of the preceding aspects, another implementation of the aspect provides, further comprising: a fourth electrode positioned adjacent to the second arm, the fourth electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a fourth driving connection connected to the fourth electrode between the proximate end and the midpoint.

[0028] Optionally, in any of the preceding aspects, another implementation of the aspect provides, further comprising a plurality of segments, the first electrode and the second electrode positioned as one segment of the plurality of segments.

[0029] In an embodiment, the disclosure includes a computing device for designing a lumped optical modulator, the computing device comprising: a first selecting means for selecting a candidate electrode length for an electrode in the lumped optical modulator; a determining means for determining a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro-optical bandwidth for the candidate electrode length; and an adjusting means for adjusting the candidate electrode length when a desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and a second selecting means for selecting the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length. [0030] Lumped optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of an optical waveguide. In most lumped optical modulators, a driver amplifier is connected to the electrode at a midpoint. An electrical signal from the driver amplifiers is applied to the electrodes. This changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. The maximum signal frequency that can be supported by a lumped optical modulator is a function of input power, modulator length, electrode length, and driver amplifier impedance. One approach to increase the maximum signal frequency is to split each electrode into multiple discontinuous segments and increase the number of driver amplifiers attached to the electrodes. Accordingly, many parameters of a lumped optical modulator can be adjusted to tune the modulator to a desired set of frequencies. Regardless of the parameter configuration, lumped optical modulators perform poorly at higher frequencies (e.g., greater than 60 gigahertz (GHz)). [0031] The present embodiment includes a mechanism for adjusting an additional parameter to tune a lumped optical modulator to operate at higher frequencies. As noted above, lumped optical modulators include driver amplifiers that are connected to the electrodes at a midpoint. This creates a pair of equal sized radio frequency (RF) cavities in the electrode on either side of the midpoint that resonate at higher frequencies. The disclosed mechanism adjusts the position of the driving connection. This alters the size of the RF cavities, and hence adjusts the resonance frequencies that can be achieved. In order to support phase matching between the electrical signal and the optical carrier wave, the driving position is located between the proximate end of the electrode (nearest the optical carrier wave input) and the midpoint of the electrode. The mechanism selects a candidate electrode length and iteratively tests various driving positions between the proximate end of the electrode and the midpoint. When the desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth achieved by such testing, candidate electrode length can be increased for further testing. When the desired electro- optical bandwidth is within a range of the maximum electro-optical bandwidth, the electrode length and driving position are known. A number of segments can then be determined based on the electrode length and the modulator length. Accordingly, the present disclosure includes an adjustable parameter and a mechanism for adjusting such a parameter to tune an optical modulator for operation at a specified set of higher frequencies without an associated increase in power. Hence, the disclosed mechanisms support an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed mechanisms can be used to create additional functionality, reduce resource usage, and/or solve problems that are specific to optical signal generation and associated component design.

[0032] Optionally, in any of the preceding aspects, another implementation of the aspect provides, the device being further configured to perform the method of any of the preceding aspects.

[0033] For the purpose of clarity, any one of the foregoing embodiments may be combined with any one or more of the other foregoing embodiments to create a new embodiment within the scope of the present disclosure.

[0034] These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts.

[0036] FIG. 1 is a schematic diagram of an example lumped optical modulator.

[0037] FIG. 2 is a schematic diagram of an example lumped optical modulator with selected driving positions.

[0038] FIG. 3 is a schematic diagram of an example segmented lumped optical modulator with selected driving positions.

[0039] FIG. 4 is a schematic diagram of an example lumped optical modulator with selected driving positions resulting in a radio frequency (RF) wave traveling in the same direction as the optical carrier.

[0040] FIG. 5 is a schematic diagram of an example lumped optical modulator with selected driving positions resulting in a RF wave traveling in the opposite direction as the optical carrier. [0041] FIG. 6 is a graph of example return loss values at various frequencies for a lumped optical modulator with an electrode powered at different driving positions.

[0042] FIG. 7 is a graph of example electrode RF response values at various frequencies for an electrode powered at different driving positions.

[0043] FIG. 8 is a graph of example electrode lengths that achieve various bandwidths for a lumped optical modulator with an electrode with a center driving position and with selected driving positions.

[0044] FIG. 9 is a schematic diagram of an example control device for designing/manufacturing a lumped optical modulator with selected driving positions.

[0045] FIG. 10 is a flowchart of an example method of designing/manufacturing a lumped optical modulator with selected driving positions.

[0046] FIG. 11 is a flowchart of another example method of designing/manufacturing a lumped optical modulator with selected driving positions.

[0047] FIG. 12 is an example of a manufacturing device for designing/manufacturing a lumped optical modulator with selected driving positions.

DETAILED DESCRIPTION

[0048] It should be understood at the outset that although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or yet to be developed. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents.

[0049] Lumped optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of an optical waveguide. In most lumped optical modulators, a driver amplifier is connected to the electrode at a midpoint. An electrical signal from the driver amplifiers is applied to the electrodes. This changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. The maximum signal frequency that can be supported by a lumped optical modulator is a function of input power, modulator length, electrode length, and driver amplifier impedance. One approach to increase the maximum signal frequency is to split each electrode into multiple discontinuous segments and increase the number of driver amplifiers attached to the electrodes. Accordingly, many parameters of a lumped optical modulator can be adjusted to tune the modulator to a desired set of frequencies. Regardless of the parameter configuration, lumped optical modulators perform poorly at higher frequencies (e.g., greater than 60 gigahertz (GHz)). [0050] Disclosed herein is a mechanism for adjusting an additional parameter to tune a lumped optical modulator to operate at higher frequencies. As noted above, lumped optical modulators include driver amplifiers that are connected to the electrodes at a midpoint. This creates a pair of equal sized radio frequency (RF) cavities in the electrode on either side of the midpoint that resonate at higher frequencies. The disclosed mechanism adjusts the position of the driving connection. This alters the size of the RF cavities, and hence adjusts the resonance frequencies that can be achieved. In order to support phase matching between the electrical signal and the optical carrier wave, the driving position is located between the proximate end of the electrode (nearest the optical carrier wave input) and the midpoint of the electrode. The mechanism selects a candidate electrode length and iteratively tests various driving positions between the proximate end of the electrode and the midpoint. When the desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth achieved by such testing, candidate electrode length can be increased for further testing. When the desired electro- optical bandwidth is within a range of the maximum electro-optical bandwidth, the electrode length and driving position are known. A number of segments can then be determined based on the electrode length and the modulator length. Accordingly, the present disclosure includes an adjustable parameter and a mechanism for adjusting such a parameter to tune an optical modulator for operation at a specified set of higher frequencies without an associated increase in power. Hence, the disclosed mechanisms support an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed mechanisms can be used to create additional functionality, reduce resource usage, and/or solve problems that are specific to optical signal generation and associated component design.

[0051] FIG. 1 is a schematic diagram of an example lumped optical modulator 100. The lumped optical modulator 100 is an optical component that creates an optical signal 103 for transmission over an optical fiber, an optical network, or other optical transmission medium. For example, the lumped optical modulator 100 is configured to receive an optical carrier 101 and modulate an electrical signal onto the optical carrier in order to create and output an optical signal 103. An optical carrier 101 is any optical wave, which may be generated by an optical source, such as a laser, diode, or other photonics component. An optical signal 103 is an optical wave with a phase and/or amplitude that has been shifted to encode corresponding data for transmission.

[0052] The lumped optical modulator 100 comprises a waveguide 110. A waveguide 110 is a transparent medium configured to refract/channel light for modulation. The waveguide 110 may comprise Silicon (Si). Specifically, the waveguide 110 comprises an upper arm and a lower arm. The optical carrier 101 is equally split between the upper arm and lower arm. This allows electrical components associated with the upper arm and lower arm to independently act on the optical carrier 101 in order to modulate corresponding portions of the optical carrier 101. The upper arm and lower arm of the waveguide 110 recombine in order to recombine the modulated optical carrier 101 to create the final optical signal 103 for output.

[0053] The lumped optical modulator 100 comprises a negatively doped (N-doped) Si region

123 and a positively doped (P-doped) Si region 121 adjacent to, and on either side of, the upper arm of the waveguide 110. The lumped optical modulator 100 also comprises a N-doped Si region 123 and a P-doped Si region 121 adjacent to, and on either side of, the lower arm of the waveguide 110. When voltage differential is applied to the N-doped Si region 123 and the P- doped Si region 121 , the movement of charge relative to the regions and the waveguide 110 cause a change in the carrier density in the materials, which alters the refractive properties of the waveguide 110 material. Specifically, the change in waveguide 110 refractive properties can reduce light intensity and/or slow light down, resulting in a change in amplitude or phase, respectively, in the optical carrier 101. This may be referred to as the carrier plasma dispersion effect. Hence, the change in the waveguide 110 refractive properties modulates the optical carrier 101 to create the optical signal 103 based on a corresponding electrical signal, which may also be referred to as a radio frequency (RF) signal.

[0054] The lumped optical modulator 100 also comprises a first electrode 126 and a second electrode 125 adjacent to the P-doped Si region 121 and the N-doped Si region 123 associated with each arm of the waveguide 110. The first electrode 126 and the second electrode 125 apply the voltage differential to the P-doped Si region 121, the N-doped Si region 123, and corresponding portion of the waveguide 110. The first electrode 126 and the second electrode 125 have a driving connection 128 and a driving connection 127, respectively. The driving connections 128 and 127 are a part of a conductive trace that connects to electrical components, such as an amplifier. Hence, the driving connections 128 and 127 receive driving voltage/current and apply such voltage/current to the first electrode 126 and the second electrode 125. The driving connections 128 and 127 are located at a driving position 129. A driving position 129 is a location where the driving connections 128 and 127 are attached to the first electrode 126 and the second electrode 125. The first electrode 126 and the second electrode 125 each have a midpoint 130 between a proximate end 122 and a distal end 124. As shown, the driving position 129 for the driving connections 128 and 127 is at the midpoint 130 of each electrode.

[0055] In a lumped optical modulator 100, the first electrode 126 and the second electrode 125 are connected to the driving connections 128 and 127, and are not further connected to additional electrical components. For example, a traveling wave modulator includes electrodes connected to resistors on the distal end 124 in the direction of the optical output. The resistor captures and dissipates RF energy to prevent the RF signal from reflecting back into the electrode. In a lumped design, the RF signal is allowed to travel to the end of the electrode and reflect back toward the midpoint 130. The lumped optical modulator 100 is more energy efficient than the traveling wave modulator due to the lack of circuitry for RF signal dissipation at the cost of increased electro-optical noise. For example, a lumped optical modulator 100 resonates at particular electrical frequencies. As such, changes in electrode length can have an effect of the operable frequencies of the lumped optical modulator 100. Further, placing the driving position 129 at the midpoint 130 creates two equal sized cavities in the corresponding electrode 126 and/or 125, where the cavities exist between the midpoint 130 and the proximate end 122 of the electrode and between the midpoint 130 and the distal end 124 of the electrode. This creates a resonance and a corresponding return loss at a resonance frequency. This return loss manifests as a failure for the lumped optical modulator 100 to modulate the optical signal 103 at the resonance frequency. The resonance frequency is a function of the length of the cavities. As such, the lumped optical modulator 100 is unable to modulate the optical signal 103 at certain frequencies that are defined by electrode 125 and 126 length as well as driving position 129. [0056] FIG. 2 is a schematic diagram of an example lumped optical modulator 200 with selected driving positions 229 and 249. The lumped optical modulator 200 is similar to the lumped optical modulator 100. For example, the lumped optical modulator 200 comprises a waveguide 210 for containing an optical carrier 201 during modulation into an optical signal 203, which are substantially similar to waveguide 110, optical carrier 101, and optical signal 103, respectively. The waveguide 210 comprises a first arm 212 and a second arm 214, each with an optical input for receiving the optical carrier 201 and an optical output for outputting the optical signal 203.

[0057] The lumped optical modulator 200 also comprises a first modulator 220 and a second modulator 240 for modulating the optical carrier 201 in the first arm 212 and the second arm 214, respectively. The first modulator 220 and the second modulator 240 are similar to the structures described with respect to the lumped optical modulator 100. The first modulator 220 comprises a first electrode 226, a second electrode 225, a P-doped Si region 221, and an N-doped Si region 223, which are substantially similar to the first electrode 126, the second electrode 125, the P- doped Si region 121, and the N-doped Si region 123, respectively. The first electrode 226 is positioned adjacent to the first arm 212. The second electrode 225 is also positioned adjacent to the first arm 212 and positioned between the first arm 212 and the second arm 214.

[0058] The first electrode 226 comprises a proximate end 222 positioned in the direction of the optical input and a distal end 224 positioned in the direction of the optical output. The first electrode 226 also comprises a midpoint 230 half way between the proximate end 222 and the distal end 224. It should be noted that the proximate end 222 and distal end 224 are directional terms included for clarity of discussion. The first modulator 220 also comprises a first driving connection 228 connected to the first electrode 226 between the proximate end 222 and the midpoint 230. The second electrode 225 comprises a proximate end 222 positioned in the direction of the optical input and a distal end 224 positioned in the direction of the optical output. The second electrode 225 also comprises a midpoint 230 half way between the proximate end 222 and the distal end 224. The first modulator 220 also comprises a second driving connection 227 connected to the second electrode 225 between the proximate end 222 and the midpoint 230. [0059] The second modulator 240 comprises a third electrode 246, a fourth electrode 245, a P-doped Si region 241, and an N-doped Si region 243, which are substantially similar to the first electrode 126, the second electrode 125, the P-doped Si region 121, and the N-doped Si region 123, respectively. The third electrode 246 is positioned adjacent to the second arm 214 and positioned between the first arm 212 and the second arm 214. The third electrode 246 comprises a proximate end 242 positioned in the direction of the optical input and a distal end 244 positioned in a direction of the optical output. The third electrode 246 also comprises a midpoint 230 half way between the proximate end 242 and the distal end 244. The second modulator 240 also comprises a third driving connection 247 connected to the third electrode 246 between the proximate end 242 and the midpoint 230. The fourth electrode 245 is positioned adjacent to the second arm 214. The fourth electrode 245 comprises a proximate end 242 positioned in the direction of the optical input and a distal end 244 positioned in a direction of the optical output. The fourth electrode 245 also comprises a midpoint 230 half way between the proximate end 242 and the distal end 244. The second modulator 240 also comprises a fourth driving connection 248 connected to the fourth electrode 245 between the proximate end 242 and the midpoint 230. [0060] As noted above, most lumped optical modulators, such as lumped optical modulator 100, include driving connections 128 and 127 located at a driving position 129 that is exactly at the midpoint 130 of the modulator. In contrast, lumped optical modulator 200 includes driving connections 227, 228, 247, and 248 that are not positioned at the midpoint 230. The driving connections 227, 228, 247, and 248 are otherwise substantially similar to driving connections 128 and 127. Specifically, the driving connections 227 and 228 are located at a driving position 229 between the proximate end 222 and the midpoint 230. Further, the driving connections 247 and 248 are located at a driving position 249 between the proximate end 242 and the midpoint 230. By moving the driving positions 229 and 249, the length of the cavities in the first electrode 226, the second electrode 225, the third electrode 246, the fourth electrode 245 change. Changing the length of a cavity alters the resonance frequency of the associated electrode. As such, adjusting the driving positions 229 and 249 alters the modulation frequencies that can be achieved by the corresponding first modulator 220 and second modulator 240, respectively. For example, both the length of the electrodes 225, 226, 245, and 246 and the driving positions 229 and 249 of the electrodes 225, 226, 245, and 246 may be adjusted until a desired set of modulation frequencies can be achieved.

[0061] It should be noted that the lumped optical modulator 200 depicts driving positions 229 and 249 as between the proximate ends 222 and 242 and the midpoint 230. The driving positions 229 and 249 may also be positioned midpoint 230 and the distal ends 224 and 244. As discussed in more detail below, positioning the driving positions 229 and 249 between the midpoint 230 and the distal ends 224 and 244 has the same effect on cavity length and resonance as equivalent positions between proximate ends 222 and 242 and the midpoint 230. However, the RF signal to be modulated should be phase matched to the optical signal 203. Such phase matching is more difficult to perform when the driving positions 229 and 249 are located between the midpoint 230 and the distal ends 224 and 244.

[0062] In summary, the lumped optical modulator 200 drives the relevant electrodes off the center line in the direction from which the light is propagating, while not fully coinciding with the propagating direction. This approach may improve electro-optical bandwidth more than twenty percent with constant modulation efficiency.

[0063] FIG. 3 is a schematic diagram of an example segmented lumped optical modulator 300 with selected driving positions. The segmented lumped optical modulator 300 comprises a first modulator 320 and a second modulator 340, which are similar to the first modulator 220 and the second modulator 240 of lumped optical modulator 200. However, the first modulator 320 and the second modulator 340 are separated into a plurality of segments. In the example shown, each modulator 320 and 340 include three segments, but any number of segments may be employed. [0064] Accordingly, the segmented lumped optical modulator 300 includes a waveguide 310, which is substantially similar to waveguide 210. The first modulator 320 is positioned adjacent to the upper arm of the waveguide 310 and the second modulator 340 is positioned adjacent to the lower arm of the waveguide 310. Each segment may be electrically isolated from adjacent segments. Each segment includes a first electrode 326 and a second electrode 325, which are substantially similar to the first electrode 226 and the second electrode 225, respectively. Each segment includes a midpoint 330, a proximate end 322, and a distal end 324, which are substantially similar to the midpoint 230, the proximate end 222, and the distal end 224, respectively. The first electrode 326 and the second electrode 325 have a first driving connection 328 and a second driving connection 327, which are substantially similar to the first driving connection 228 and the second driving connection 227, respectively. Further, each segment includes a driving position 329, which is the location where the driving connection 328 and 327 connect to the corresponding electrode. As shown, each segment includes a driving position 329 positioned between the proximate end 322 and the midpoint 330. As such, the driving position 329 of each segment of each modulator can be adjusted to alter the achievable modulation frequencies for the segmented lumped optical modulator 300.

[0065] It should be noted that the third electrode 246 and the fourth electrode 245 can be implemented as one or more segments in the second modulator 340 in the same manner as the implementation of the first electrode 326 and the second electrode 325 are implemented as one or more segments in the first modulator 320.

[0066] FIG. 4 is a schematic diagram of an example lumped optical modulator 400 with selected driving positions resulting in a RF wave traveling in the same direction as the optical carrier. The lumped optical modulator 400 comprises a first modulator 420 and a second modulator 440, which are similar to the first modulator 220 and the second modulator 240 of lumped optical modulator 200. The lumped optical modulator 400 also comprises a waveguide 410 with a first arm 412 and a second arm 414, which are substantially similar to waveguide 210, first arm 212, and second arm 214, respectively. The waveguide 410 comprises an optical input for receiving an optical carrier 401 and an optical output for outputting an optical signal 403, which are substantially similar to optical carrier 201 and optical signal 203, respectively. The first modulator 420 and the second modulator 440 each comprise a proximate end 422 and a distal end 424. The first modulator 420 and the second modulator 440 also comprise a midpoint 430 halfway between the proximate end 422 and the distal end 424. The first modulator 420 and the second modulator 440 also comprise driving positions 429, which are substantially similar to driving positions 229 and 249. As shown, the driving positions 429 are between the proximate end 422 and the midpoint 430.

[0067] In the example shown, the optical carrier 401 travels from left to right during modulation to become the optical signal 403. Further, the RF signal 405 is received from other parts of the circuitry. The RF signal 405 is the driving electrical signal modulated onto the optical carrier 401 by the first modulator 420 and the second modulator 440 to create the optical signal 403. As shown, the RF signal 405 moves between the driving positions 429 while being modulated onto the optical carrier 401. Since the driving positions 429 are near the proximate end 422, the RF signal 405 moves in a counter-clockwise direction. As such, when the RF signal 405 enters the corresponding modulator, the RF signal 405 initially moves from left to right in the same direction as the optical carrier 401. One of the issues with optical modulation is that the phase of the RF signal 405 should be matched to the phase of the optical carrier 401 to result in a clear optical signal 403. This can place design constraints on the lumped optical modulator 400 because electricity and light travel at different speeds. Because the RF signal 405 moves in the same direction as the optical carrier 401, phase matching becomes much simpler from a design perspective. Further, positioning the driving positions 429 between the proximate end 422 and the midpoint 430 has the same effect from an electrical resonance perspective as positioning the driving positions 429 between the distal end 424 and the midpoint 430.

[0068] FIG. 5 is a schematic diagram of an example lumped optical modulator 500 with selected driving positions resulting in a RF wave traveling in the opposite direction as the optical carrier. The lumped optical modulator 500 comprises a first modulator 520 and a second modulator 540, which are similar to the first modulator 220 and the second modulator 240 of lumped optical modulator 200. The lumped optical modulator 500 also comprises a waveguide 510 with a first arm 512 and a second arm 514, which are substantially similar to waveguide 210, first arm 212, and second arm 214, respectively. The waveguide 510 comprises an optical input for receiving an optical carrier 501 and an optical output for outputting an optical signal 503, which are substantially similar to optical carrier 201 and optical signal 203, respectively. The first modulator 520 and the second modulator 540 each comprise a proximate end 522 and a distal end 524. The first modulator 520 and the second modulator 540 also comprise a midpoint 530 halfway between the proximate end 522 and the distal end 524. The first modulator 520 and the second modulator 540 also comprise driving positions 529, which are substantially similar to driving positions 229 and 249. The lumped optical modulator 500 is substantially similar to the lumped optical modulator 400, except the driving positions 529 are between the distal end 524 and the midpoint 530. [0069] The lumped optical modulator 500 receives an RF signal 505 from other parts of the circuitry. The RF signal 505 is the driving electrical signal that is modulated onto the optical carrier 501 by the first modulator 520 and the second modulator 540 to create the optical signal 503. In the example shown, the optical carrier 501 travels from left to right during modulation to become the optical signal 503. However, since the driving positions 529 are between the distal end 524 and the midpoint 530, the RF signal 505 moves in a clockwise direction (the opposite of lumped optical modulator 400). Accordingly, when the RF signal 505 enters the corresponding modulator, the RF signal 505 initially moves from right to left in the opposite direction as the optical carrier 501. Since the RF signal 505 moves in the opposite direction from the optical signal 503, matching the phase between the two signals is problematic. As noted above, positioning the driving positions 529 between the distal end 524 and the midpoint 530 has the same effect from an electrical resonance perspective as positioning the driving positions 529 between the proximate end 522 and the midpoint 530. Accordingly, the lumped optical modulator 400 and 500 are substantially similar from an electrical resonance standpoint, but the lumped optical modulator 400 provides beneficial phase matching properties over lumped optical modulator 500.

[0070] In summary, when performing same direction modulation according to lumped optical modulator 400, the RF signal 505 and light travel in the same direction. This results in a good phase match while supporting maximization of the modulation efficiency. In contrast, when performing opposite-direction modulation according to lumped optical modulator 500, the RF signal 505 and light travel in the opposite direction. This results in a large phase mismatch, which can create penalties for modulation efficiency. In a lumped electrode launching from the midpoint 430/530, the two direction RF waves always exist, so the overall modulation includes both of the above two types modulation. Considering the difference in modulation efficiency, the same-direction modulation contributes more benefits than opposite-direction modulation, especially at high RF frequency.

[0071] FIG. 6 is a graph 600 of example return loss values at various frequencies for a lumped optical modulator with an electrode powered at different driving positions. For example, graph 600 may result when driving positions for a lumped optical modulator 100, 200, 300, 400, and/or 500 are shifted from the midpoint toward the proximate and/or distal ends. Graph 600 shows return loss in decibels (dBs), which indicates the amount of energy used in an electrode. When the electrode resonates, the RF energy suffers from destructive interference and is lost. As such, the dips in graph 600 indicate the frequencies, depicted in gigahertz (GHz), where resonance occurs. As can be seen, different driving positions result in different resonance frequencies.

[0072] For example, driver source impedance (Zs) plays a significant role in lumped electrode design for high baud rate applications. This implies that the connection between the driver and modulator electrode is important. In many cases, copper pillars and solder balls may be preferred when employing flip-chip bonding and/or monolithic integration. Wire bond connections may introduce uncontrollable parasitic impedances like capacitance and inductance. For example, assuming an electrode length of 400 micrometers (pm) with P-doped and N-doped (PN) doping, a frequency-dependent RF response may improve dramatically when impedance is reduced from thirty ohms to five ohms. The modulation efficiency is constant at low frequency, but the EO bandwidth increases monotonously when impedance decreases. High bandwidth applications generally prefer low source impedance.

[0073] In a limiting driver/invertor design, implementing a low output impedance may use large transistor area, which may result in large power consumption and reduce the driver speed. In any event, an impedance of ten ohms was selected as default driver setting in the analysis that resulted in graph 600. In the example analysis, ideal transmission lines are constructed by 400 micrometer (um) electrodes, which are connected to the source with 10-ohm impedance by copper pillars with 25 pm diameter and 45 pm pitch. As shown in graph 600, the return loss is nearly zero dB everywhere with sharp dips at specific frequencies. This implies that all RF driving signals are fully reflected back except for some frequencies which resonate in the electrode. The Cu-pillars break the electrode and form two cavities. The travelling electric signal is transmitted and/or reflected among cavities. The transmitted and reflected signals interfere with each other, which leads to a strong resonance at frequencies corresponding to the cavity lengths. This resonance is shown here as a return loss dip at resonance frequency.

[0074] When return loss for different copper pillar locations at the electrode is displayed, the evolution of RF performance is noticeable. If a copper pillar is located at the center of the electrode, the two cavities are identical and the dip of return loss (the first resonance dip) is located at the highest frequency, which may be preferred for a lumped electrode design. When the copper pillar location is shifted away from the electrode center, the return loss dip moves toward lower frequencies because the length of one cavity increases.

[0075] In a modulator design, the PN junction is added to generate free carrier modulation. Transmission lines are constructed in the same way. Namely PN doping is represented by an equivalent circuit, and is implemented by lumped electrical elements. PN doping between two electrodes results in a much lower RF propagation velocity, leading to a shift of first resonance dip toward much lower frequency. If a cu-pillar is located at the center of the electrode, the first resonance dip is located at the highest frequency. When the cu-pillar location is shifted away from the electrode center, the first resonance dip moves toward lower frequencies. Accordingly, two RF cavities are formed by a driving point and two open ends. The first resonant frequency is roughly determined by the cavity with the longest electrode. The electrode with a middle driving position results in the highest resonance frequency.

[0076] FIG. 7 is a graph 700 of example electrode RF response values at various frequencies for an electrode powered at different driving positions. For example, graph 700 may result when driving positions for a lumped optical modulator 100, 200, 300, 400, and/or 500 are shifted from the midpoint toward the proximate and/or distal ends. Graph 700 shows an RF response of an electrode in dBs at various frequencies in GHz when the driving position changes. As shown, the effective operational frequencies of the optical modulator changes depending on the driving position of the electrodes.

[0077] For example, to examine how resonance effect can help EO response, one may look to the average RF signal strength along the electrode actually applied to the optical signal. To monitor the overall signal on the electrode, the average voltage along the electrode can be used to calculate the RF response based on the equation below:

where V_ave is the average voltage along the electrode, Vin is the input voltage, and S 2 l_ave is the RF response of the optical modulator.

[0078] In graph 700, the driving position is varied from the proximate end to the distal end by a corresponding connection pad sweeping from zero to one. As shown, the RF response shows a maximum 3dB bandwidth at the midpoint and no peaking appears. Further, when the driving point is moved away from the middle, the 3dB bandwidth decreases with peaking up to 4dB. The performance of the RF response is identical as long as the distance from driving point to the middle is the same due to the symmetry of the structure. No electrical difference is seen on the proximate side or the distal side.

[0079] The RF response at different location is displayed for a 400 pm electrode connected to the source at 100 pm position with cu-pillar. The energy distribution along the electrode is remarkable, and the average RF response curve is obtained for this cu-pillar location. By changing the cu-pillar location in the electrode from 50 pm away from the end to 200 pm (in the electrode center), average RF response vs. frequency is compared. The design with the flattest RF response with the lowest resonance peak (where the return loss shows the first dip) is observed when the RF source is connected to the electrode center. When the connection point is off the center, the corresponding resonance peak shows up in the RF response curve with decreased bandwidth.

[0080] For example, at low frequencies (<40GHz), the RF loss is very low because the power of the RF backward wave is similar to the RF forward wave. Further, when the light travels through the electrodes at low frequencies, the relative direction of the light and the direction RF wave does not matter. However, at higher frequencies (>40GHz), the RF loss in the transmission line is no longer negligible. The power of backward RF wave becomes lower than the forward RF wave. As such, the same-direction modulation from the forward RF wave generates higher optical modulation than the opposite-direction modulation from the backward RF wave. When the RF frequency increases, the RF propagation loss becomes larger and the same-direction modulation design is more effective than the opposite-direction modulation design. In the high frequency scenario, the modulator with matching RF/light direction shows much better performance. The above analysis shows that, to get highest RF electrode response bandwidth by taking advantage of RF resonance, positioning the driving position on the electrode closer to the middle (X=0.5) may be preferable to take advantage of the RF-cavity effect. Further, a light traveling direction coinciding to RF driving forward wave has larger OE bandwidth due to the phase-match effect.

[0081] The disclosed electrode design considers both the RF-cavity effect and phase-match effect. For example, the parameter X may represent the RF driving position on the electrode. In the modeling X may vary from 0 (proximate end) to 1 (distal end). In an example lumped optical modulator, bandwidth increases to a maximum of 72 GHz with X=0.4 from a reference 58G EO bandwidth with X=0.5. The EO response over frequency is smooth for this example, which results in an optical modulator that operates over a broad set of frequencies.

[0082] The length of a lumped electrode is a significant parameter in modulator design. A long electrode increases the DC modulation efficiency while reducing the EO bandwidth. Depending on the requirements of an application, different electrode lengths may be selected in the modulator design. For an example electrode length from 200 pm to 800 pm, the RF driving position Xpad max may be searched independently to determine the maximum EO bandwidth for each length. In this example, the Xpad_max is in the range of 0.2 to 0.4, depending on electrode length.

[0083] FIG. 8 is a graph 800 of example electrode lengths that achieve various band widths for a lumped optical modulator with an electrode with a center driving position and with selected driving positions. For example, graph 800 may result when driving positions for a lumped optical modulator 100, 200, 300, 400, and/or 500 are shifted from the midpoint toward the proximate and/or distal ends. Graph 800 shows electrode lengths between 250 pm and 800 pm that result in a target bandwidth in GHz. Specifically, the bottom line shows such electrode lengths when a center driving position is used and the top line shows such electrode lengths when a driving position is selected to according to the present disclosure. As can be seen, determining and selecting a driving position between the proximate end and the midpoint supports longer electrode lengths (increasing modulation efficiency) for a similar EO bandwidth achieved by an electrode with a center driving position. The factor of EO bandwidth enhancement is more than twenty percent over almost all EO bandwidths.

[0084] Further, the disclosed design can increase electrode length by twenty eight percent at a 50 GHz target EO bandwidth and by eight percent at 80 GHz target EO bandwidth. For a 100 GHz baud application with a 75 GHz target EO bandwidth, the disclosed design increases driving efficiency about fifty eight percent.

[0085] FIG. 9 is a schematic diagram of an example control device 900 for designing/manufacturing a lumped optical modulator with selected driving positions, such as lumped optical modulator 200, 300, 400, and/or 500. For example, control device 900 can be used to implement a method 1000, method 1100 and/or manufacturing device 1200. Hence, the control device 900 is suitable for implementing the disclosed examples/embodiments as described herein. The control device 900 comprises downstream ports 920, upstream ports 950, and/or one or more transceiver units (Tx/Rx) 910, including transmitters and/or receivers for communicating data upstream and/or downstream over a network. The control device 900 also includes a processor 930 including a logic unit and/or central processing unit (CPU) to process the data and a memory 932 for storing the data. The control device 900 may also comprise optical-to-electrical (OE) components, electrical-to-optical (EO) components, and/or wireless communication components coupled to the upstream ports 950 and/or downstream ports 920 for communication of data via electrical, optical, and/or wireless communication networks.

[0086] The processor 930 is implemented by hardware and software. The processor 930 may be implemented as one or more CPU chips, cores (e.g., as a multi-core processor), field- programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), digital signal processors (DSPs), or any combination of the foregoing. The processor 930 is in communication with the downstream ports 920, Tx/Rx 910, upstream ports 950, and memory 932. The Tx/Rx 910 comprises a control module 914. The control module 914 implements the disclosed embodiments described herein. Specifically, the control module 914 may be employed to design a lumped optical modulator by adjusting the driving position, electrode length, and/or the number of segments to tune the lumped optical modulator to operate at a predetermined set of frequencies that are out of range for other Si photonics devices. Accordingly, the control module 914 may be configured to perform mechanisms to address one or more of the problems discussed above. As such, the control module 914 improves the functionality of the control device 900 as well as addresses problems that are specific to the optical communication arts. Further, the control module 914 effects a transformation of the control device 900 to a different state. Alternatively, the control module 914 can be implemented as instructions stored in the memory 932 and executed by the processor 930 (e.g., as a computer program product stored on a non-transitory medium).

[0087] The memory 932 comprises one or more memory types such as disks, tape drives, solid-state drives, read only memory (ROM), random access memory (RAM), flash memory, ternary content-addressable memory (TCAM), static random-access memory (SRAM), and other optical and/or electrical memory systems suitable for this task. The memory 932 may be used as an over-flow data storage device, to store programs when such programs are selected for execution, and to store instructions and data that are read during program execution.

[0088] FIG. 10 is a flowchart of an example method 1000 of designing/manufacturing a lumped optical modulator with selected driving positions, such as lumped optical modulator 100, 200, 300, 400, and/or 500, for example by employing a control device 900 and/or a manufacturing device 1200. Method 1000 may assume the modulator doping, transmission line dimension, and source impedance Zs are fixed for simplicity. Method 1000 employs the following notation. X=(0~1) indicates a driving position on an electrode between the proximate end at 0 and the distal end at 1. Lset indicates electrode length. EOBW indicates EO bandwidth. EOBWtarget indicates atarget EO bandwidth design (e.g. 75GHz for lOOGbaud). OO indicates a converge factor. Ltotal indicates a total electrode length. Nseg indicates a minimum number of segments with EOBW>=EOBWtarget.

[0089] At step 1001, a candidate electrode length is set to a minimum value. At step 1003, the driving position X is swept between the proximate end 0 and the midpoint 0.5 to determine the EO bandwidths that can be obtained at the candidate electrode length. At step 1005, the driving position X for the maximum EO bandwidth is determined at the candidate electrode length. At step 1007, the maximum EO bandwidth is compared to the target EO bandwidth. When the difference is out of range (greater than or equal to a parameter esp), the method 1000 proceeds to step 1009. At step 1009, the candidate electrode length is increased. For example, the electrode length can be increased by a constant (c) times a ratio of the EO bandwidth divided by the target EO bandwidth for the design. The method may then return to step 1003 to determine the driving positions and EO bandwidths for the new candidate electrode length.

[0090] Returning to step 1007, when the difference between the maximum EO bandwidth and the target EO bandwidth is not out of range (less than a parameters esp), the method 1000 may proceed to step 1011. At step 1011, the electrode length, driving position, and EO bandwidth are selected. At step 1013, the number of segments for the modulator are determined. For example, the minimum number of segments (Nseg) is determined according to a ceiling function that divides a predetermined total length of the modulator (Ltotal) by the selected electrode length. Accordingly, the electrode length, driving position, number of segments, and the resulting EO bandwidth (which meets the target spec) are known at the conclusion of step 1013. [0091] FIG. 11 is a flowchart of another example method 1100 of designing/manufacturing a lumped optical modulator with selected driving positions, such as lumped optical modulator 200, 300, 400, and/or 500, for example by employing a control device 900 and/or a manufacturing device 1200. Method 1100 may begin when a device determines to design a lumped optical modulator.

[0092] At step 1101, the device selects a candidate electrode length for an electrode in the lumped optical modulator. For example, the candidate electrode length may be between 200 pm to 800 pm. At step 1103, the device determines a driving position between a proximate end of the electrode and a midpoint of the electrode. The determined driving position results in a maximum electro-optical bandwidth for the candidate electrode length selected at step 1101. The lumped optical modulator may comprise an optical input for receiving an optical carrier wave for modulation and an optical output for outputting an optical signal. The proximate end of the electrode is positioned toward the optical input and away from the optical output. Determine the driving position at step 1103 may include iteratively testing a resulting electro-optical bandwidth for each candidate driving position between the proximate end of the electrode and the midpoint of the electrode. The candidate driving position with a largest resulting electro-optical bandwidth can then be determined as the driving position resulting in the maximum electro-optical bandwidth for the candidate electrode length. The driving position creates RF cavities in the electrode that resonate at corresponding frequencies. So iteratively testing may include determining the resulting electro-optical bandwidth corresponding to resonance of the RF cavities based on RF cavity length.

[0093] At step 1105, the device adjusts the candidate electrode length when a desired electro- optical bandwidth is not within a predetermined range of the maximum electro-optical bandwidth for the candidate electrode length. At step 1107, the device selects the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the predetermined range of the maximum electro-optical bandwidth for the candidate electrode length. At step 1109, the device determines a number of electrode segments for the selected candidate electrode length resulting in a segmented electrode of a total length of the lumped optical modulator. [0094] It should be noted that the lumped optical modulator is not a traveling wave optical modulator and hence does not comprise a terminal resistor connected to the electrode. Further, the electrode may be connected to a driving amplifier by a copper pillar, solder ball, or flipchip bonding at the driving position.

[0095] FIG. 12 is an example of a manufacturing device 1200 for designing/manufacturing a lumped optical modulator with selected driving positions, such as lumped optical modulator 200, 300, 400, and/or 500. For example, the manufacturing device 1200 may perform the steps of method 1000 and/or 1100 and/or may be implemented on and/or in conjunction with a control device 900. The manufacturing device 1200 comprises a first selecting module 1201 for selecting a candidate electrode length for an electrode in the lumped optical modulator. The manufacturing device 1200 also comprises a determining module 1203 for determining a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro-optical bandwidth for the candidate electrode length. The manufacturing device 1200 also comprises an adjusting module 1205 for adjusting the candidate electrode length when a desired electro-optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length. The manufacturing device 1200 also comprises a second selecting module 1207 for selecting the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

[0096] A first component is directly coupled to a second component when there are no intervening components, except for a line, a trace, or another medium between the first component and the second component. The first component is indirectly coupled to the second component when there are intervening components other than a line, a trace, or another medium between the first component and the second component. The term “coupled” and its variants include both directly coupled and indirectly coupled. The use of the term “about” means a range including ±10% of the subsequent number unless otherwise stated.

[0097] It should also be understood that the steps of the exemplary methods set forth herein are not necessarily required to be performed in the order described, and the order of the steps of such methods should be understood to be merely exemplary. Likewise, additional steps may be included in such methods, and certain steps may be omitted or combined, in methods consistent with various embodiments of the present disclosure.

[0098] While several embodiments have been provided in the present disclosure, it may be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented.

[0099] In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, components, techniques, or methods without departing from the scope of the present disclosure. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and may be made without departing from the spirit and scope disclosed herein.

Claims

CLAIMS What is claimed is:

1. A method of designing a lumped optical modulator, the method comprising: selecting, by a processor, a candidate electrode length for an electrode in the lumped optical modulator; determining, by the processor, a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro- optical bandwidth for the candidate electrode length; adjusting, by the processor, the candidate electrode length when a desired electro- optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and selecting, by the processor, the candidate electrode length and the driving position when the desired electro -optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

2. The method of claim 1, further comprising determining, by the processor, a number of electrode segments for the selected candidate electrode length resulting in a segmented electrode of a total length of the lumped optical modulator.

3. The method of any of claims 1-2, the lumped optical modulator comprising an optical input for receiving an optical carrier wave for modulation and an optical output for outputting an optical signal, the proximate end of the electrode positioned toward the optical input and away from the optical output.

4. The method of any of claims 1-3, the determining the driving position comprising: iteratively testing a resulting electro-optical bandwidth for each candidate driving position between the proximate end of the electrode and the midpoint of the electrode; and determining the candidate driving position with a largest resulting electro-optical bandwidth as the driving position resulting in the maximum electro-optical bandwidth for the candidate electrode length.

5. The method of any of claims 1-4, the driving position creating radio frequency (RF) cavities in the electrode that resonate at corresponding frequencies, the iteratively testing comprising determining the resulting electro-optical bandwidth corresponding to resonance of the RF cavities based on RF cavity length.

6. The method of any of claims 1-5, the lumped optical modulator not comprising a terminal resistor connected to the electrode.

7. The method of any of claims 1-6, further comprising connecting the electrode to a driving amplifier by a copper pillar, solder ball, or flipchip bonding at the driving position.

8. A lumped optical modulator designed by a process of: selecting, by a processor, a candidate electrode length for an electrode in the lumped optical modulator; determining, by the processor, a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro- optical bandwidth for the candidate electrode length; adjusting, by the processor, the candidate electrode length when a desired electro- optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and selecting, by the processor, the candidate electrode length and the driving position when the desired electro -optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

9. The lumped optical modulator of claim 8, the process further comprising determining, by the processor, a number of electrode segments for the selected candidate electrode length resulting in a segmented electrode of a total length of the lumped optical modulator.

10. The lumped optical modulator of any of claims 8-9, the lumped optical modulator comprising an optical input for receiving an optical carrier wave for modulation and an optical output for outputting an optical signal, the proximate end of the electrode positioned toward the optical input and away from the optical output.

11. The lumped optical modulator of any of claims 8-10, the determining the driving position comprising: iteratively testing a resulting electro-optical bandwidth for each candidate driving position between the proximate end of the electrode and the midpoint of the electrode; and determining the candidate driving position with a largest resulting electro-optical bandwidth as the driving position resulting in the maximum electro-optical bandwidth for the candidate electrode length.

12. The lumped optical modulator of any of claims 8-11, the driving position creating radio frequency (RF) cavities in the electrode that resonate at corresponding frequencies, the iteratively testing comprising determining the resulting electro-optical bandwidth corresponding to resonance of the RF cavities based on RF cavity length.

13. The lumped optical modulator of any of claims 8-12, the lumped optical modulator not comprising a terminal resistor connected to the electrode.

14. The lumped optical modulator of any of claims 8-14, the process further comprising connecting the electrode to a driving amplifier by a copper pillar, solder ball, or flipchip bonding at the driving position.

15. A lumped optical modulator comprising: an optical waveguide comprising a first arm with an optical input and an optical output; and a first electrode positioned adjacent to the first arm, the first electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a first driving connection connected to the first electrode between the proximate end and the midpoint.

16. The lumped optical modulator of claim 15, the optical waveguide further comprising a second arm with an optical input and an optical output, and the lumped optical modulator further comprising: a second electrode positioned between the first arm and the second arm, the second electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a second driving connection connected to the second electrode between the proximate end and the midpoint.

17. The lumped optical modulator of any of claims claim 15-16, further comprising: a third electrode positioned between the first arm and the second arm, the third electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a third driving connection connected to the third electrode between the proximate end and the midpoint.

18. The lumped optical modulator of any of claims claim 15-17, further comprising: a fourth electrode positioned adjacent to the second arm, the fourth electrode comprising a proximate end positioned in a direction of the optical input, a distal end positioned in a direction of the optical output, a midpoint between the proximate end and the distal end; and a fourth driving connection connected to the fourth electrode between the proximate end and the midpoint.

19. The lumped optical modulator of any of claims claim 15-18, further comprising a plurality of segments, the first electrode and the second electrode positioned as one segment of the plurality of segments.

20. A computing device for designing a lumped optical modulator, the computing device comprising: a first selecting means for selecting a candidate electrode length for an electrode in the lumped optical modulator; a determining means for determining a driving position between a proximate end of the electrode and a midpoint of the electrode, the driving position resulting in a maximum electro- optical bandwidth for the candidate electrode length; and an adjusting means for adjusting the candidate electrode length when a desired electro- optical bandwidth is not within a range of the maximum electro-optical bandwidth for the candidate electrode length; and a second selecting means for selecting the candidate electrode length and the driving position when the desired electro-optical bandwidth is within the range of the maximum electro-optical bandwidth for the candidate electrode length.

21. The computing device of claim 21, the device being further configured to perform the method of any of claims 1-7.